Kelly Ripa’s search for a new Live! co-host is starting four months earlier than previously announced – and for a reason.

Ripa’s morning talk show costar Michael Strahan will end his nearly four years on Live! this Friday, despite initial plans for him to stay on through September before beginning a new role at Good Morning America.

The 45-year-old tells PEOPLE in this week’s cover story, on newsstands Friday, that she and Live! staff members – whom she affectionately refers to as “family” – served as the impetus behind the decision to speed up Strahan’s departure.

“What we’ve explained to them is, ‘Well, if you had asked us, we would have told you, Guys, we need to start looking, because we have summer hiatus, we have vacation time. We need to find people. If we’re going to have this list narrowed down at least to a manageable size by the fall, we need to start now,'” Ripa explains, noting, “nobody consulted us initially.”

News of Strahan’s plans to leave the long-running ABC show broke publicly in mid-April – the same day that Ripa, herself, found out. Despite the immediate fallout, Strahan and Ripa continued on, side by side, just a week later, with the star calling the situation a prime example of why workplace communication is crucial.

Now, the task at hand is finding a replacement for Strahan, 44, that matches the pair’s “chemistry and camaraderie.” Numerous stars have had their hats thrown in the ring, with a source previously telling PEOPLE that Ripa would “love” for pal Anderson Cooper to join her behind the Live! desk.

Cooper, 48, has insisted that he’s “very happy at CNN,” but Ripa sheepishly grinned while telling PEOPLE of getting the star on board: “Stay tuned … “

“We just keep doing it one show at a time,” she says of keeping the show afloat amid the hunt. “We always try to remind ourselves it’s never as good as we think it is and it’s never as bad as we think it is. We just keep marching forward. That’s what we’ve done for years. It’s not a formula I invented. This is a formula that Regis [Philbin] created, and we’re sticking to it.”

Until a decision is made, Live! already has several interim co-hosts signed on. First up to the plate? Jimmy Kimmel, who will join Ripa for the show on Monday.